Design and development of reversible data hiding schemes are widely studied topic due to its wide scope in cloud computing and medical image transmission. This paper introduces a new reversible data hiding algorithm based on the histogram of the blocks of the cover images with an efficient overflow management technique. In the new scheme, the peak intensity value from each block is used for data hiding, and to make sure the correct recovery of the original image, the grayscale value used for data hiding from each block is embedded in the same block itself by replacing the least significant bits of eight selected pixels. The lossless recovery is ensured by embedding those least significant bits in the same block itself along with the secret message. Detailed theoretical analysis and experimental study of the scheme are carried out and discussed in this paper. The images from the standard image dataset of the University of Southern California (USC-SIPI) are used in our study.